Itay Glazer

activity

20162026

most citedOn singularity properties of convolutions of algebraic morphisms

8 citations · 28 across the 15 of their papers we have counts for

collaborators

17 papers

math.PR2026

Anti-concentration of polynomials: $L^{p}$ balls and symmetric measures

Itay Glazer, Dan Mikulincer

We begin with the observation, based on previous results, that dimension-free lower bounds on the variance of a polynomial under a log-concave measure yield dimension-free small-ba…

math.RT2026

On Harish-Chandra's integrability theorem in positive characteristic

Avraham Aizenbud, Dmitry Gourevitch, David Kazhdan +3

The celebrated Harish-Chandra's integrability theorem states that the distributional character of an irreducible smooth representation of a p-adic group $G (F)$ is integrable, that…

math.AG2025

A lower bound on the analytic log-canonical threshold over local fields of positive characteristic

Itay Glazer, Yotam I. Hendel

Given a local field $F$ of positive characteristic, an $F$ -analytic manifold $X$ and an analytic function $f : X \to F$ , the $F$ -analytic log-canonical threshold $\mathrm{lct}…

math.GR2025

Word maps and random words

Emmanuel Breuillard, Itay Glazer

We discuss some recent results by a number of authors regarding word maps on algebraic groups and finite simple groups, their mixing properties and the geometry of their fibers, em…

math.NT2024

Eventual tightness of projective dimension growth bounds: quadratic in the degree

Raf Cluckers, Itay Glazer

In projective dimension growth results, one bounds the number of rational points of height at most $H$ on an irreducible hypersurface in $P^{n}$ of degree $d > 3$ by $C(n)d^2 H…

math.GR2024

Fourier and small ball estimates for word maps on unitary groups

Nir Avni, Itay Glazer, Michael Larsen

To a non-trivial word $w (x_{1}, ..., x_{r})$ in a free group $F_{r}$ on $r$ elements and a group $G$ , one can associate the word map $w_{G} : G^{r} \to G$ that takes an $r$ -tupl…

math.RT2023

Integrability and singularities of Harish-Chandra characters

Itay Glazer, Julia Gordon, Yotam I. Hendel

Let $G$ be a reductive group over a local field $F$ of characteristic $0$ . By Harish-Chandra's regularity theorem, the character $Θ_{π}$ of an irreducible, admissible representation…

math.PR2022

On the Fourier coefficients of word maps on unitary groups

Nir Avni, Itay Glazer

Given a word $w (x_{1}, \dots, x_{r})$ , i.e., an element in the free group on $r$ elements, and an integer $d \geq 1$ , we study the characteristic polynomial of the random matrix $w(X_…

math.AG2022★ 1 cited

Integrability of pushforward measures by analytic maps

Itay Glazer, Yotam I. Hendel, Sasha Sodin

Given a map $ϕ : X \to Y$ between $F$ -analytic manifolds over a local field $F$ of characteristic $0$ , we introduce an invariant $ε_{⋆} (ϕ)$ which quantifies the integrabil…

math.PR2021

Anti-concentration of polynomials: dimension-free covariance bounds and decay of Fourier coefficients

Itay Glazer, Dan Mikulincer

We study random variables of the form $f (X)$ , when $f$ is a degree $d$ polynomial, and $X$ is a random vector on $R^{n}$ , motivated towards a deeper understanding of the c…

math.AG2021

A number theoretic characterization of $E$ -smooth and (FRS) morphisms: estimates on the number of $Z / p^{k} Z$ -points

Raf Cluckers, Itay Glazer, Yotam I. Hendel

We provide uniform estimates on the number of $Z / p^{k} Z$ -points lying on fibers of flat morphisms between smooth varieties whose fibers have rational singularitie…

math.GR2020

Pro-isomorphic zeta functions of nilpotent groups and Lie rings under base extension

Mark N. Berman, Itay Glazer, Michael M. Schein

We consider pro-isomorphic zeta functions of the groups $Γ (O_{K})$ , where $Γ$ is a unipotent group scheme defined over $Z$ and $K$ varies over all number fields. U…

math.AG2019★ 2 cited

On singularity properties of word maps and applications to probabilistic Waring type problems

Itay Glazer, Yotam I. Hendel

We study singularity properties of word maps on semisimple algebraic groups and Lie algebras, generalizing the work of Aizenbud-Avni in the case of the commutator map. Given a word…

math.AG2018★ 7 cited

On singularity properties of convolutions of algebraic morphisms -- the general case (with an appendix joint with Gady Kozma)

Itay Glazer, Yotam I. Hendel

Let $K$ be a field of characteristic zero, $X$ and $Y$ be smooth $K$ -varieties, and let $G$ be a algebraic $K$ -group. Given two algebraic morphisms $φ : X \to G$ and $ψ:Y\righ…

math.AG2018★ 8 cited

On singularity properties of convolutions of algebraic morphisms

Itay Glazer, Yotam I. Hendel

Let $K$ be a field of characteristic zero, $X$ and $Y$ be smooth $K$ -varieties, and let $V$ be a finite dimensional $K$ -vector space. For two algebraic morphisms $φ : X \to V$ …

math.AG2017★ 6 cited

On rational singularities and counting points of schemes over finite rings

Itay Glazer

We study the connection between the singularities of a finite type $Z$ -scheme X and the asymptotic point count of X over various finite rings. In particular, if the generi…

math.RT2016★ 4 cited

Representations of reductive groups distinguished by symmetric subgroups

Itay Glazer

Let $G$ be a complex reductive group and $H = G^{θ}$ be its fixed point subgroup under a Galois involution $θ$ . We show that any $H$ -distinguished representation $π$ (i.e $\mathrm{dim}…

Anti-concentration of polynomials: Lp balls and symmetric measures

On Harish-Chandra's integrability theorem in positive characteristic

A lower bound on the analytic log-canonical threshold over local fields of positive characteristic

Word maps and random words

Eventual tightness of projective dimension growth bounds: quadratic in the degree

Fourier and small ball estimates for word maps on unitary groups

Integrability and singularities of Harish-Chandra characters

On the Fourier coefficients of word maps on unitary groups

Integrability of pushforward measures by analytic maps

Anti-concentration of polynomials: dimension-free covariance bounds and decay of Fourier coefficients

A number theoretic characterization of E-smooth and (FRS) morphisms: estimates on the number of Z/pkZ-points

Pro-isomorphic zeta functions of nilpotent groups and Lie rings under base extension

On singularity properties of word maps and applications to probabilistic Waring type problems

On singularity properties of convolutions of algebraic morphisms -- the general case (with an appendix joint with Gady Kozma)

On singularity properties of convolutions of algebraic morphisms

On rational singularities and counting points of schemes over finite rings

Representations of reductive groups distinguished by symmetric subgroups

Anti-concentration of polynomials: $L^{p}$ balls and symmetric measures

A number theoretic characterization of $E$ -smooth and (FRS) morphisms: estimates on the number of $Z / p^{k} Z$ -points